Interpolating methods based on other criteria such as smoothness need not yield the most likely intermediate values. Example of one-dimensional data interpolation by kriging, with confidence intervals. Squares indicate the location of the data. The kriging interpolation, shown in spatial statistics and geostatistics pdf, runs along the means of the normally distributed confidence intervals shown in gray.
The dashed curve shows a spline that is smooth, but departs significantly from the expected intermediate values given by those means. Krige sought to estimate the most likely distribution of gold based on samples from a few boreholes. The basic idea of kriging is to predict the value of a function at a given point by computing a weighted average of the known values of the function in the neighborhood of the point. Even so, they are useful in different frameworks: kriging is made for estimation of a single realization of a random field, while regression models are based on multiple observations of a multivariate data set.
The difference with the classical kriging approach is provided by the interpretation: while the spline is motivated by a minimum norm interpolation based on a Hilbert space structure, kriging is motivated by an expected squared prediction error based on a stochastic model. Gaussian process evaluated at the spatial location of two points. Gaussian, with a mean and covariance that can be simply computed from the observed values, their variance, and the kernel matrix derived from the prior. In geostatistical models, sampled data is interpreted as the result of a random process. The first step in geostatistical modulation is to create a random process that best describes the set of observed data.